Question: What is the next term of the geometric sequence? $-\dfrac{128}{27},\dfrac{32}{9},-\dfrac83,$
In a geometric sequence there's a constant ratio between subsequent terms. Let's find that ratio, and use it to find which term should come after the last one that is given, which is $-\dfrac83$. Each term is ${-\dfrac34}$ times the term before it. ${\times \left(-\dfrac34\right)\,\curvearrowright}$ ${\times \left(-\dfrac34\right)\,\curvearrowright}$ $-\dfrac{128}{27},$ $\dfrac{32}{9},$ $-\dfrac83$ So the next term is $-\dfrac83\cdot\left({-\dfrac34}\right)=2$. The missing term is $2$.